Novel analogue-based and geostatistical approaches for space-time prediction of environmental variables

In many environmental applications, it is important to obtain accurate and coherent reconstructions of environmental maps. These can be for example spatial representations of hydrological variables or satellite-based remote sensing products. To do this, analogue-based methods provide a fast and interpretable approach that is based on replicating patterns coming from historical observations and predictor similarity. However, their classical weighted-average aggregation tends to smooth spatial variability and attenuate extremes. This study evaluates whether analogue-based reconstruction of MODIS evapotranspiration (ET) over the Ebro watershed can be improved through local analogue selection and stochastic pattern-based aggregation. Several strategies are compared, including domain-wise and tile-wise analogue selection, inverse-distance weighted averaging, and two Multiple-Point Statistics simulation techniques, chessQS and a new method named Anchor Sampling. Weighted averaging provides the best pixel-wise accuracy, image-structure agreement, and computational efficiency, while tile-wise analogue selection yields only marginal improvements over domain-wise selection. Anchor Sampling offers the most balanced stochastic option, improving variogram agreement, timestep water-balance error, and tail-value statistics while remaining closer to the deterministic baseline than chessQS. In contrast, chessQS increases spatial flexibility but reduces reconstruction accuracy and image-structure agreement in the present application. The results indicate that stochastic aggregation can help preserve aspects of spatial variability and distributions, but that simple analogue averaging remains a strong baseline for ET map reconstruction, unless the realism of the spatial structure or uncertainty representation are specifically required.